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The original and most common method to transpose horizontal to tilted diffuse irradiance is based on the Isotropic Sky Model (ISM). Various aspects of the ISM are explored here, including the connection between the ideal isotropic sky radiance distribution and the corresponding diffuse irradiance on a tilted collector. By completing an extensive literature review of the ISM, its origin and history are clearly established, and the methods of derivation are discussed. The oldest known derivations of the ISM are identified. In particular, the landmark contribution of Liu and Jordan (1960) is found not to be the original source of the ISM transposition formula, even though it is usually credited for it. The ISM significance is discussed in the present context of solar energy applications, where the accuracy of irradiance calculations is critical. A detailed review of the methods of derivation, including boundary conditions, is proposed to explain differing results and remove all sources of confusion that have permeated the literature. Lastly, the use of anisotropic models is advocated to avoid unnecessary systematic errors.